Download xcxcx

Alternative Approaches
for Integration of Models
Elena Rovenskaya
IIASA Advanced Systems
Analysis Program
Sometimes multi-model approach
is necessary…
Paradigm shifts by Kuhn: successive change of one model
by another, rather than integration of different paradigms
Progress of science:
from single- to multi-model approach
Some examples from natural
science…
• theory of light: from vibration of ether
to wave-particle duality
• laws of motion: from Newton’s
dynamics to Schrödinger’s and
Heisenberg’s formalism
In social and environmental sciences appreciation
of the multi-model approach is to be obtained
Example: multi-model approach for
sustainable forest management
Orange area is the Pareto area for the PPA model, blue area is
the Pareto area for the model with no feedback (IIASA project
on optimization of forest management)
The relationship between economic benefit and ecological
value is rather different in two similar models
Evolution of modeling paradigm
single-model approach
Belief in
one model
multi-model approach
Comparison
of models
Integration of
models
Models integration: formalization
Model 1
Output 1
Model 2
Output 2
Input
Synthetic
signal
based on output
1 and output 2
• Output 1 and output 2 represent the model results for the
same real quantity
• Output 1 does not coincide with output 2
• Output 1 and output 2 can be either deterministic or
stochastic, either scalar or vector, either finite or infinite
dimensional variable
Basing on the past approach
• Approximate the past history by two models’ outcomes
and extrapolate the obtained approximation into the
future
С , С = Arg min x − C1 x1 − C2 x2
*
1
*
2
C1 ,C 2
x ≅ C x +C x
*
1 1
*
2 2
Example
• Nordhaus’s DICE-model (nonlinear!) as a generator of
“real” data with the terminal GDP as a model’s output
• Two one-dimensional linear models of the global GDP
The blue, red and green bars represent relative errors
in terminal GDP for 50 testing controls in case the
learning database consists of 10, 50 and 100 controls
correspondingly (IIASA project on integration of
models)
Distribution-based approach
• Compare the distributions of models’ outputs with the joint
distribution => in case the joint distribution has lower
variance, use its expectation
Lower joint variance => compatible models
Higher joint variance => incompatible models
Example
• Integration of the Landscape Ecosystems Approach (LEA)
and Stochastic Modeling Approach (SMA) of net primary
production of the Russian forest-tundra
The blue and red curves show the NPP distributions (in
grams of carbon per square meter per year) given by
LEA and SMA, respectively. The green curve shows the
integrated distribution formed using the posterior
integration analysis technique (IIASA YSSP project on
integration of models)
“Calculus of models”
• Objects:
models
• Actions:
linking (IAM), integration, approximation,…
THANK YOU FOR YOUR ATTENTION!
I welcome your comments,
suggestions, ideas…
[email protected]